To solve the exercise, first we are going to write the composition of the functions:
[tex]\begin{gathered} \text{ Given two functions }f(x)\text{ and }g(x)\colon \\ f\lbrack g(x)\rbrack=(f\circ g)(x) \end{gathered}[/tex]It reads "f composed of g", simply said "we are going to fill f with g":
So, in this case, we have
[tex]\begin{gathered} f(x)=\frac{48}{x^2}-\frac{12}{x}+1 \\ g(x)=2x \\ f\lbrack g(x)\rbrack=\frac{48}{(2x)^2}-\frac{12}{2x}+1 \\ f\lbrack g(x)\rbrack=\frac{48}{4x^2}-\frac{12}{2x}+1 \\ \text{ Simplifying} \\ f\lbrack g(x)\rbrack=\frac{12}{x^2}-\frac{6}{x}+1 \end{gathered}[/tex]Now, we evaluate, that is, we replace x = 2 in the composite function and operate
[tex]\begin{gathered} f\lbrack g(2)\rbrack=\frac{12}{(-2)^2}-\frac{6}{-2}+1 \\ f\lbrack g(2)\rbrack=\frac{12}{4}+3+1 \\ f\lbrack g(2)\rbrack=3+3+1 \end{gathered}[/tex]Therefore,
[tex]f\lbrack g(2)\rbrack=7[/tex]